Calculate the thermal stresses in steel:

Calculate the thermal stresses in steel & copper while the temperature of the assembly is increased to 45^oC.

Solution

In this case, while the temperature of the assembly is increased, copper shall expand more than steel and therefore, shall exert a thrust on the steel nut and bolt head therefore generating tension in the steel. As there is no other external force this tension ought to be kept in equilibrium by the compressive force induced in copper. Therefore  by formulating the compatibility condition of whole strains (thermal + elastic) the problem might be solved out.

Assume forces induced in steel & copper be designated as P_s & P_c respectively in kN units.

Thermal strain in steel,

ε_st  = α_s  × ΔT

= 12 × 10^{- 6}  × (40 - 15)

= 3 × 10^{- 4}  m/m

Thermal strain in copper, α_c  × ΔT

= 18 × 10^{- 6}  × (40 - 15)

= 4.5 × 10^{- 4}  m/m

Elastic strain in steel, δ_se  =     P_s / A_s E_s

=          Ps/ (π/4) × 182 × 200

Elastic strain in copper, δ_ce = 1.965 × 10- 5 Ps

=          Pc/ A_s E_c

= P_c / (π/4) × (30² - 18²) 120= 1.8421 × 10^{- 5} P_c